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Progress In Electromagnetics Research B, Vol. 53, 291–314, 2013
FAULT PREDICTION OF DEEP BAR CAGE ROTORINDUCTION MOTOR BASED ON FEM
Basil Saied1 and Ahmed Ali2, *
1Electrical Engineering Department, University of Mosul, Iraq2Foundation of Technical Education, Technical College of Engineering,Mosul, Iraq
Abstract—The paper aims to investigate the use of the FiniteElement Method for electrical and mechanical faults detection inthree-phase squirrel cage, induction machines. The features of FiniteElement Method are significant, which consider the physical mappingof stator winding and rotor bar distribution. Therefore, modelingof the faults in stator winding, rotor bars and air-gap eccentricitywill be predicated in more accurate way. In comparison withconventional methods such as coupling method, the Finite ElementMethod considers the complex machine geometry, material type of thebar, current and the flux distributions within the electrical machines.As a result, the air-gap eccentricity and the broken bars can be modeledeffectively using this approach. Motor current signature analysis hasbeen used to give a decision about the fault occurrence. For thebroken rotor bar, frequency of the sideband components around thefundamental is used to indicate the presence of fault. However, thesideband frequencies cannot be used to recognize the stator windingshort circuit and eccentricities faults, where the harmonics haveapproximately the same frequency over the spectrum. The amplitudeof the sideband harmonic components have been used to differentiatebetween them. It has been found that the inter-turn short circuitfaults have a sideband harmonic component with amplitude greaterthan that in the case of the air-gap eccentricity faults. Also currentpaper introduces the detection of broken rotor bars based on statorcurrent envelope technique.
Received 19 June 2013, Accepted 30 July 2013, Scheduled 6 August 2013* Corresponding author: Ahmed Ali ([email protected]).
292 Saied and Ali
1. INTRODUCTION
Three-phase cage rotor, induction machines have wide spreadingon industrial applications due to their low cost and maintenancerequirements, ability to work in polluted environments and rigidity.The electrical machine has to be monitored so that faults can bepredicted as early as possible, and consequently the machine and itsfunction can be protected. Mechanical and electrical faults can occurin this type of machines; the mechanical faults represent about 50%of the faults [1, 2]. Bearing is one of the most occurring mechanicalfaults. In advance stage, it will cause severe air-gap eccentricity [3].The electrical faults can take place on both stator and rotor. Themain types of these faults are inter-turn short circuit of stator winding,which represents about 30%, and broken bar, which represents about10%. Finally, 10% of the faults represent external faults [4]. The maintypes of the electric machines faults are detected by analyzing thestator current [5, 6]. For all faults eccentricity types, two parametersare considered to indicate the type of faults, which are the frequencyand amplitude of the harmonics in the spectrum of the stator current.The classical methods had been used to determine the frequency ofthe sideband harmonics correctly. Due to approximation criteria usedin these methods, the amplitude of the sideband harmonics has aconsiderable deviation from the experimental methods [7, 8].
Numerical methods were used to determine the parameters ofelectrical machines such as magnetic coupling method and winding andextended winding function methods that give more accurate resultsthan analytical approach. Complex geometry, non-linear behavior ofcore materials and actual representation of winding distribution on thestator slots can be efficiently modeled using FEM. This will provide anaccurate calculation of electromagnetic fields and as a consequence allthe machine parameters. FEM is used to determine the linear or non-linear behaviors of electromagnetic fields by solving a set of Maxwell’sequations. In this paper, a two-dimensional model is considered toconstruct the geometry of three-phase cage-type induction motor basedon finite element transient analysis.
The operation of three-phase induction motor using transit finiteelement analysis was considered. The motor current signature analysis(MCSA) was employed to detect the mixed air-gap eccentricity [1].The static and dynamic eccentricities were simulated using timestepping finite element method (TSFEM). These types of faults weredetected based on the amplitude of sideband harmonics componentsaround fundamental component and principle slot harmonic (PSH).It was proven that the amplitude of sideband components around
Progress In Electromagnetics Research B, Vol. 53, 2013 293
the fundamental harmonic could be used as a factor to detect thefault occurrence without its type, while the amplitude of the sidebandharmonics components on PSH and around it can be used to detectthe air-gap eccentricity fault and its type [2]. A 2-D FEM was used tosimulate and analyze the performance of electric machine. Solution ofelectromagnetic filed equations provides acceptable information abouthealthy and inter-turn short circuit. The winding in each phase wasdivided into different groups in order to model the different types ofshort circuit fault. The coils of stator phases are divided into two partsconnected in series with equal turns for each part. By this method,a short circuit can be implemented at any location of the coil [5].FEM considers a powerful tool used to model and study different typeof broken rotor bars. It was found that this type of faults changesthe distribution of the losses on stator core and the distribution ofthe current on the rotor circuit. In addition, the rotor bars circuitis subjected to the thermal effect in case of adjacent broken rotorbars [6]. In the case of inter-turn stator winding fault, the distributionof magnetic field parameters was distorted, and the stored energy isreduced when the severity of winding increases [9]. Magneto-staticanalysis based on finite element analysis is used to determine thevariation of the flux and stored energy in the electric machines [9, 10].Based on this type of analysis, the variation of the magnetic flux,magnetic flux density and stored energy can be computed accurately.A complete model of a cage-rotor three-phase squirrel induction motorwas modeled using MagNet. Due to the broken bars, the distribution ofthe magnetic force on the slot teeth near the broken bars was reduced.In addition, increasing the number of broken bars leads to reduce thestored magnetic energy [10].
In the current paper, FEM has been used to simulate anddetect the main types of faults in three-phase squirrel cage inductionmachines. FEM is used to build the complex geometry of the model,and the type of materials is selected to specify the stator windings,rotor bars and iron cores. As a result, all electrical and mechanicalfaults types can be modeled smoothly based on this numerical method.MCSA has been used to give a decision about the fault occurrence.In case of broken rotor bar, the sideband frequency componentsaround the fundamental give indication about the attendance of fault.Additionally, a detection of broken rotor bars based on stator currentenvelope technique has been introduced. In case of the air-gapeccentricity and stator winding short circuit faults, the harmonics haveapproximately the same sidebands components over the spectrum. Ithas been found that the inter-turn short circuit faults have a sidebandharmonic component at k = 4 with amplitude greater than that in
294 Saied and Ali
the case of the air-gap eccentricity faults. This factor can be used torecognize between these types of faults.
2. TYPES OF INDUCTION MOTOR FAULTS
In the current paper, the following common types of inductionmachines faults are presented.
2.1. Broken Rotor Bar Faults
These common faults occur on the movement part of cage rotor type orsynchronous machine, which has damper bars. Cracking or breakingthese bars arises due to manufacturing problem on the bar itself ordue to high value of bar currents which induce through rotor circuits.These currents are caused by unbalanced, sudden or over loading ofthe machine. It had been shown that the broken bar may affect thematerial properties of the core and the current distribution of theadjacent rotor bars. Therefore, the adjacent bar is more susceptible tobreak than the nonadjacent bar.
2.2. Stator Winding Faults
In this type of faults, a short circuit could occur between two adjacentturns, coils or even between phases. In advanced stage, faults maytake place between the core and the stator windings. Harmonicscomponents of the flux density in the air-gap region may be used to givean indication about the stator turn faults. As a result, the magneticflux as well as flux density will be deformed, and stored magneticenergy will decrease in proportion to the degree of short circuit [9].Therefore, it is possible to diagnose the faults of induction machinesby analyzing the magnetic field quantities.
2.3. Air-gap Eccentricity Faults
In this kind of faults, the air-gap of the machine has unequal spacesalong the outer radius of rotor. Air-gap eccentricity faults may occurdue to damage of the mechanical parts of the electric machine likethe gearbox bearings. These misalignments of the shaft include staticeccentricity, dynamic eccentricity or mixed eccentricity. In staticeccentricity, although the axial axis of the rotor coincides with theaxial axis of rotation, it does not coincide with stator axis, and theminimum air-gap position is fixed. In dynamic eccentricity, the rotoraxial axis does not coincide with the axis of rotation, and the minimumair-gap position rotates along the internal boundary of the stator.
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In mixed eccentricity, both the stator and rotor axial axes coincidebetween the two axes of rotations. The frequencies of the harmonicsaround the fundamental component give good indication that thereis an eccentricity fault type, while the amplitude of the sidebandharmonics around the PSH indicates the type of eccentricity.
3. FAULT ANALYSIS TECHNIQUES
3.1. Park Method (PM)
In this technique, three-phase stator currents is transformed into two-phase system using the following equations:
iα =
√23iA −
√16iB −
√16iC (1)
iβ =
√12iB −
√12iC (2)
In the normal case of machine operation, without fault, the relationbetween the two currents in the Eqs. (1) and (2) have approximatelya circle shape centered at the origin. For the abnormal operatingconditions (such as single phasing, short circuit of stator winding,broken bars or air-gap eccentricity), the three-phase stator currentsbecome unbalanced, which produce an oscillation in the radius of thePark vector, by substituting the instantaneous values of three-phasestator currents in Eqs. (1) and (2). Therefore, the trajectory deviatesfrom circle to elliptic form [1]. The degree of deviation and the axialangle of the elliptic locus depend on the severity degree and type ofthe faults.
3.2. Fast Fourier Transform Method
This method is adopted in the present paper to analyze the statorcurrent. Then the frequency spectrum of this current is studied toobtain information about it. Depending on the sideband harmonics ofthe analyzed current, the type of fault can be predicted. Fast Fouriertransform has been used to scan the frequencies and amplitudes, aswell as the frequency spectrum, of stator line current [1–6].
3.3. Envelope of the Three-phase Stator Current
In addition to frequency analysis of stator current to detect the faultsof induction machines, the envelope of the stator current is a helpfulcharacteristic for fault classification. The stator current envelope of
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the three-phase induction machine is used to identify the number ofbroken bars. The envelope signal is the change in amplitude for thestator currents due to fault occurrence. Therefore, the frequency of theenvelope can be used as an indication to estimate the number brokenbars.
Due to broken rotor bars, the envelope is generated in the statorcurrents. It is repeated regularly at a frequency given by:
fenv = 2Sfs (3)
4. MATHEMATICAL MODEL OF ELECTRICALMACHINE USING MAXWELL’S EQUATIONS
Figure 1 shows the finite element model of the motor that has beenused in simulation. The main formulas used in time stepping finiteelement analysis (TSFEA) are the Ampere law and conservation offlux density law [11, 12]:
∇×H = J (4)∇ ·B = 0 (5)
∇×E = −∂B∂t
(6)
whereH is the magnetic field intensity vector (A/m);J is the current density vector (Amp/m2);B is the magnetic flux density vector (wb/m2);E is the electric field intensity vector (volt/m).The above equation can be rewritten in terms of the magnetic
vector potential A (web/m), where:B = ∇×A (7)
Figure 1. Finite element model of the motor section under simulation.
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Substituting Eq. (7) in Eqs. (6) and (4) gives [13]:
∇×(
1µ∇×A
)= J (8)
∇ (∇ ·A)−∇2A = µJ (9)
µ is the magnetic permeability of the material.Applying vector notation, where ∇(∇ ·A) = 0, gives the Poisson
equation:∇2A = −µJ (10)
The current density (J = 0) in the air-gap region, which gives theLaplace Equation as follows:
∇2A = 0 (11)
The power circuit elements have been coupled directly to the finiteelement region through coupling nodes [14]. ANSYS software providesa library of electrical elements (CIRCU124) for building the electricpower circuit.
5. MODELING OF DEEP BAR INDUCTION MACHINE
5.1. Two-dimensional Assumptions for Finite ElementModel
In order to reduce the simulation time without loss of the accuracy ofthe results, it is important to consider some assumptions for modelingprocess. A 2-D finite element method has been used to construct thegeometry of the machine. For this modeling type, it is assumed thatthe current density J has only one component in z-direction, (Jz), andcan be written in the following form:
J = (0, 0,Jz) (12)
The magnetic vector potential A has also one component (Az) in thesame direction of Jz, then:
A = (0, 0,Az) (13)
According to these assumptions, the magnetic flux density andmagnetic flux intensity will have two components in the xy-plane (Bx,By, Hx, Hy) as given in the following equations, where Az and Jz areperpendicular to this plane.
B = (Bx,By, 0) (14)H = (Hx,Hy, 0) (15)
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To simulate the materials of the stator slots regions, it is assumedthat the stator windings consist of small cross sectional copper wires.Eq. (10) has been modified according to this assumption and may berewrite in the following form:
− 1µ
(∂2Az
∂x2+
∂2Az
∂y2
)= Jz (16)
where, µ is the permeability of core material. In the air-gap region,the right hand term of Eq. (16) is equal to zero. Therefore, there is noinduced current in this region.
For transient analysis, in addition to the previous assumptions, ithas been assumed that the current density in the rotor region has avariable distribution over the rotor bars due to skin effect. Therefore,Eq. (16) can be modified to the following form:
∂2Az
∂x2+
∂2Az
∂y2= −
(µJz +
∂
∂tµAz
)(17)
Eq. (17) is the governing equation that has been used to model thefield distribution of the deep bar, three-phase induction motor with2D finite element analysis model. The current density of Eq. (17)consists of two terms; the first is due to applied voltage on the statorwinding while the other is the induced current in the conductor due totime variation of magnetic field.
5.2. Electric Circuit of Induction Motor
Stranded coils are used to simulate the effect of the induced emf inthe stator windings. It is assumed that the stator winding of each coilconsists of conductors with small cross section area. These conductorsare grouped together to form the stranded coil. It is assumed thattheir contribution to the current density is averaged over the area ofthe winding. To represent a voltage fed device, circuit equations mustbe coupled with the field equations. Finite Elements Model (FEM)has been coupled directly to the supply circuit.
Since a 2-D finite element model has been used to assemble thegeometry construction of the induction motor, the end winding andend ring parameters are not included in the model [15, 16]. The endparameters, especially end winding resistance, have a considerableeffect on the dynamic performance of the motor at load conditions [17].Thus, these parameters have been included in the external electriccircuits, which are coupled directly with finite element domain [18].
For dynamic modeling of electrical motors using FEM, theelectrical circuit and magnetic field domain should be coupled. In
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this work, the electric circuit has been built by using ANSY circuitelements library.
5.3. Calculation of Developed Torque
The developed torque has been computed by means of Maxwell’s stresstensor. For a 2-D finite element model, the stress tensor has beenintegrated along the middle of the air-gap lg. Because of the numericalnature of the finite element method, the result may depend on boththe position of the integrating line and the number of chosen nodes forthe numerical integration. Then the torque is [19]:
Te =ls
gµoP
∫
lg
rBrBt · ds (18)
ls is stack length (m);g is the air-gap length (m);P is the number of pole pairs;r is the mean air-gap radius (m);Br is the radial component of the flux density (wb/m2);Bt is the tangential component of the flux density (wb/m2).
The developed torque has been determined and used to calculatethe angular speed on the rotor by solving the mechanical equation ofrotation wm. The dynamic equation of induction motor that couplesbetween the electromagnetic torque and mechanical parameters isgiven by [20–22];
Te = Jdwm
dt+ Bwm + TL (19)
where
Te is the developed electromagnetic torque (N·m);TL is the steady-state load torque (N·m);B is the viscous friction ((N·m)/rad/sec);wm is the mechanical rotor speed (rad/sec).
wm =1P
dθm
dt(20)
θm is the angular position of the rotor (in electrical radius);P is the number of pole pairs.
300 Saied and Ali
6. FAULTS DETECTION TECHNIQUES BASED ON FEM
Monitoring the operation of electrical machines is an important processfor protecting this equipment from damages. Different parameters hadbeen calculated to detect the faults on electrical machines. Thesecalculations are based on the FEM in which the magnetic field variationis used to provide information about the stator and rotor currents,rotation and dynamic performance of the machine. In addition, FEMcalculates the stored magnetic energy on the machine parts in order topredict the faults [23]. As a result, FEM is adopted in the presentpaper to determine the stator current, and then by using Fouriertransform [24, 25] the frequency spectrum of the stator current isinvestigated. Depending on the sideband harmonics of the analyzedstator current, the type of fault has been predicted.
In the current research, three types of faults have beeninvestigated. The first type is the broken rotor bars, which havebeen considered. As a result of this fault, the rotor bars currentwill reduce due to increasing the total impedance of the rotor barcircuit. Therefore, the rotor circuit will have an unbalanced operation,consequently the sideband components contained in the spectrum ofthe stator current. The frequency of these harmonics ‘fb’ depends ona slip speed ‘S’ and stator current frequency ‘fs’. These sidebandcomponents are injected in the stator current.
The equation can be used to represent two sideband componentsin terms of frequency as follows:
fb = fs(1± 2KS) K = 1, 2, 3 . . . . (21)The second type is the inter-turn short circuit on stator winding, whichoccurs due to aging, overloading or manufacturing. A short circuitmay take place between some turns of stator coils of the same phaseor with other two phases. The resultant stator MMF will be affectedby this fault, and another harmonic component will be contained onstator current. The frequency ‘fsc’ of sidebands due to inter-turn shortcircuit has been calculated using the relation [6]:
fsc ={
K ± (1− S)n
P
}fs (22)
wherefsc is the short circuit frequency (Hz);n is integer = 1, 2, 3, . . . , (2P − 1);K = 1, 3, 5, . . . .The last type of faults is the air-gap eccentricity, which consists of
three types, Static Eccentricity (SE), Dynamic Eccentricity (DE) andmixed Eccentricity (ME).
Progress In Electromagnetics Research B, Vol. 53, 2013 301
air-gap
Rotor
Stator
Motor shaft
(a) (b) (c)
Figure 2. Geometry of induction motor, (a) healthy motor, (b) staticeccentricity, (c) dynamic eccentricity.
It is a familiar rotor fault, which produces a pulsation in rotorspeed of induction machine due to ripple torque. The noise andvibration are produced due to misalignment of the rotor along thegeometric centre of the stator. These faults are due to the rotordeviation from the axial axis of the stator, deflection of rotor shaft,and movement of the stator frame. The air-gap eccentricity producesunbalance of radial forces which causes friction between stator androtor windings. As a result, a damage of rotor bar and stator windingoccurs. Figure 2 illustrates the rotation of rotor in the presence ofair-gap eccentricity.
Under normal operation of the three-phase induction motor, therotating magnetic field contains the fundamental components of thestator and rotor MMFs. Due to eccentricity fault, the resultantmagnetic motive force (mmf) waveform is deviated, compared withnormal condition, and the mmf space harmonic components areaffected significantly. This will produce unbalanced distribution of themagnetic flux within the air gap. As a result, the rotating magneticfield in the air-gap consists of the fundamental components in additionto the harmonics components due to fault. The general formula ofeccentricity components fecc in the stator current is given by [2, 8].
fecc = fs
[(KNr ± nd)
(1− S)P
± ν
](23)
where
nd is the eccentricity order (nd = 0 for static eccentricity);
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Nr is the number of rotor slots;υ is the time harmonic of stator mmf = 1, 3, 5, . . . ;K is any integer (K = 1, 2, 3, . . . ).
The amplitude of harmonics components depends on the typeand degree of the eccentricity. In the case of static eccentricity, thefrequency (fecc) of the harmonic components is given by:
fecc = fs
[(KNr)
(1− S)P
± ν
](24)
7. MODELING OF CAGE TYPE INDUCTION MOTOR
The first step for fault diagnosis process is to construct a model, whichgives an accurate representation of the electrical machine. Mechanicalelements of the machine as well as the coupling equations of theelectromagnetic device should be included in the proposed model.Three main conventional methods had been used for machine modelingin the field of fault diagnosis. The magnetic coupling method (MCM),Winding Function Method (WFM), Extended Winding FunctionMethod (EWFM) and finite element method (FEM) had been used tosimulate the induction motor under healthy and faulty conditions [26–28]. The classical methods of modeling and simulation are simple, easyto manipulate and give approximate results because they are based onapproximation criteria. The basic equations of these techniques, incase of uniform air-gap, are different for non-uniform air-gap. Also theelectrical machine is assumed to work in linear region where the effectof saturation is not considered.
In the FEM, the magnetic field distribution, non-linearity ofcore materials and saturation effects are taken into consideration.Therefore, faults detection based on magnetic property variation canbe taken into account. In the present work, a Time Stepping FiniteElement Analysis (TSFEA) has been used to model the healthy andfaulty motor. This method is used to calculate the magnetic fielddistribution within the different parts of the machine to obtain theactual values of stator currents, power loss, magnetic energy, speedand dynamic torque [29–32].
8. MODELING OF INDUCTION MOTOR UNDERFAULT CONDITIONS
Finite element method offers special ability to model and study thefaults occurring in electrical machines. It provides a way to study the
Progress In Electromagnetics Research B, Vol. 53, 2013 303
performance, supervise and diagnosis different types of faults. FEMprovides a simulation condition that can be used to control all theexternal environments as well as the structure of the electric machine.
Considering the modeling of cage rotor type three-phase inductionmotor, three types of faults, broken-bars, inter-turn short circuitof stator winding and air-gap eccentricity have been modeled usingANSYS software. The modeling procedure that has been followed toform these faults can be explained as follows.
In the first type of fault, the broken bars of the rotor are modeledwith high resistivity material, and as a result, very low current actuallywill still pass through the faulty bar. Lost current in the electricalcircuit of the rotor will produce unbalance currents in the other circuitbranches; as a result, the magnetic flux and magnetic flux density inthe air-gap region will be distorted. This distortion will inject sidebandharmonics with the fundamental MMF component. The effect of theseharmonics will be transferred to the stator current, which will alsocontain harmonics due to this fault. The value of the low frequencycurrent harmonics can be calculated using Eq. (21). The amplitude ofthe harmonics depends on the slip speed of the motor and the numberof broken bars.
In the second type of faults, short circuit in stator winding mayoccur due to the damage in the insulator of stator winding, bent of therotor or negative sequence current. To simulate the short circuit faulton stator winding, it is necessary to reduce the winding number of thecoils. ANSYS software provides a command (rmodif) for modifying thenumber of winding for each stator slot. As a result, a direct modelinghas been implemented to simulate the faults between two turns or coils,single phasing and line-to-line. The order of harmonic componentsof the stator currents have been detected based on Eq. (22). Earlydetection of this fault could reduce the maintenance requirements aswell as increase the lifetime of the motor. The amplitudes of harmoniccomponents, which can be predicted by using FEM, give an indicationto the winding fault conditions.
The third type of fault is air-gap eccentricity, which can beproduced due to manufacturing or due to unbalance forces on therotor by external torques on the rotor shaft. The usual method fordetecting this type of faults is based on monitor the current signatureof stator current. Two parameters give a significant effect on this typeof fault: the frequency of the produced harmonics and the amplitudeof these components. Eq. (24) has been used to detect the harmonicsorder due to this fault. A dynamic eccentricity using FEM has beenmodeled by changing the axial axis of rotor from coincidence withboth stator and rotor rotation axes of the machine. The mixed faults
304 Saied and Ali
of induction motor have also been included and analyzed in this work.Mixed faults prediction includes static eccentricity with two brokenbars, static eccentricity with four broken bars, static eccentricity and10% inter turn short circuit of stator winding.
9. SIMULATION RESULTS
A three-phase, cage rotor type, 4-pole, 36-stator slot, double-layer, 28-rotor bar, induction machine has been used in the present simulation.The parameters of the 3-phase, 380 V, Y-connection, 18.5 kW inductionmotor are given in Table 1. A 2-D, transient analysis has been usedto solve a set of Maxwell’s equations based on FEM. The magneticfields over the model have been calculated, and as a result, all statorand rotor parameters have been obtained. The time variations of statorcurrent at no-load and rated load under healthy condition are explainedin Figures 3(a), (b). The frequency spectrum of stator line current forhealthy motor is shown in Figure 4.
In addition, simulated results for faulty motor are presented,which consider both singular and multi-faults in the following sections.
1 1.05 1.1 1.15 1.2 1.25 1.3
-50
-40
-30
-20
-10
0
10
20
30
40
50
time (s)
Sta
tor
cu
rre
nt
(A)
(a)
1 1.05 1.1 1.15 1.2 1.25 1.3
-20
-15
-10
-5
0
5
10
15
20
time (s)
Sta
tor
cu
rre
nt
(A)
(b)
Figure 3. Time variation of stator current under steady statecondition, (a) load condition, (b) no-load condition.
Table 1. Data of the induction machine used in the simulation.
Rated voltage 380 V-Y Outer radius of stator 135mm
Output power 18.5 kw Outer radius of rotor 88.4 mm
Pair pole 2 Stack length 180mm
Rated speed 1460 rpm Connection Star
Supply frequency 50Hz Rated torque 100Nm
Rated supply current 35 A-Y
Progress In Electromagnetics Research B, Vol. 53, 2013 305
20 40 60 80 100 120 140 160-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
frequency (Hz)
Am
plu
in d
B
FFT of the Signal in dB
-30 dB-37 dB
Figure 4. Frequency spectrum of stator current for healthy motorunder load condition.
9.1. Separated Faults
9.1.1. Broken Rotor Bar Results
The resistivity of rotor bars in the case of faulty motor has beenassumed to have a high value. Fast Fourier transform has been used todetermine the frequency and amplitude of the frequency spectrum ofstator line current. The time variations of stator current for two andfour broken bars are shown in Figure 5.
1 1.05 1.1 1.15 1.2 1.25 1.3-80
-60
-40
-20
0
20
40
60
80
time (s)
Sta
tor
cu
rre
nt
(A)
(a)
1 1.05 1.1 1.15 1.2 1.25 1.3-80
-60
-40
-20
0
20
40
60
80
time (s)
Sta
tor
cu
rre
nt
(A)
(b)
Figure 5. The stator current, (a) 2-broken bar condition, (b) 4-brokenbar condition.
The stator line current at rotor speed 1440 rpm has a ripple shapedue to fault. The increasing number of broken bars leads to increasingthe severity of ripple. The frequency spectrum for this fault has a twoside-band harmonic according to Eq. (21) as explained in Figure 6.The left component LSH is on 44.05 Hz, while the right one RSH is on55.55Hz for two broken bars. In the second case, for four brokenbars, the left and right components are on 44.48 Hz and 57.56 Hz,
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0 20 40 60 80 100 120 140 160 180 200-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (Hz)
Am
plitu
de
in
dB
Normalized Amplitude spectrum in dB
LSH -44.4 dB
RSH -55.03 dB
(a)
0 20 40 60 80 100 120 140 160 180 200-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (Hz)
Am
plitu
de
in
dB
LSH-43.86 dB
RSH-36.56 dB
(b)
Normalized Amplitude spectrum in dB
Figure 6. The frequency spectrum of stator current for (a) 2-brokenbar condition, (b) 4-broken bar condition.
Table 2. The amplitude and frequency variation under broken barsfaults.
Rotor
speed
(rpm)
LSH
(dB)
Frequency
(Hz)
RSH
(dB)
Frequency
(Hz)
Two
broken Bar1440 −26.56 44.05 −28.5 55.55
Four
broken Bar1420 −23.77 44.48 −27.74 57.56
Table 3. The frequency comparison between FEM and analyticalresults.
No. of
Broken
Bars
Motor
Speed
(rpm)
slip
RLSH (Hz) RSH (Hz)
FEMAnalytic
FormulaFEM
Analytic
Formula
Two broken
bars1423 0.05133 44.05 44.866 55.55 55.133
Four
broken bars1391 0.07266 42.48 42.7333 57.56 57.266
respectively. The amplitude and frequency of the sidebands harmonicscomponents are given in Table 2.
To validate the simulation, a comparison between the resultsobtained from finite element solution and analytical formula in Eq. (21)is illustrates in Table 3.
Progress In Electromagnetics Research B, Vol. 53, 2013 307
9.1.2. Stator Short Circuit Windings
Stator slots of the motor have a double coil on each slot. In the presentwork, a short circuit has been assumed between two adjacent coilsreferred to the same phase. Since the number of stator windings dueto fault is reduced, the stator current will increase. Consequently,two harmonics components will appear on the frequency spectrum ofstator current. The value of these sidebands can be calculated usingEq. (22). This type of faults will produce unbalance on the numberof winding with respect to other phases. As a result, the amplitude ofsideband harmonics components is increased. Figures 7 and 8 presentthe results, stator current and its spectrum, for 30% and 15% of interturn short circuit fault respectively.
The other healthy phases stator currents are slightly affected. The
1 1.05 1.1 1.15 1.2 1.25 1.3-80
-60
-40
-20
0
20
40
60
80
time (s)
Sta
tor
cu
rre
nt
(A)
(a)
0 50 100 150 200 250 300-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (Hz)
Am
plitu
de
in
dB
Normalized Amplitude spectrum in dB
3rd harmonic -25.06 dB
RSH-41.15 dB
LSH
-41.73 dB
(b)
Figure 7. The inter-turn short circuit (30%) condition, (a) timevariation, (b) frequency spectrum.
1 1.05 1.1 1.15 1.2 1.25 1.3
-60
-40
-20
0
20
40
60
time (s)
Sta
tor
cu
rre
nt
(A)
(a)
0 50 100 150 200 250 300-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (Hz)
Am
plitu
de
in
dB
Normalized Amplitude spectrum in dB
RSH
-40.93 dBLSH
-42.83 dB
3rd harmonic
-27 dB
(b)
Figure 8. The inter-turn short circuit (15% ) condition, (a) the timevariation, (b) the frequency spectrum.
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2 2.01 2.02 2.03 2.04 2.05 2.06-80
-60
-40
-20
0
20
40
60
80
time (s)
Sta
tor
Ph
ase
Cu
rre
nts
(A
) Healthy Phase CurrentFaulty Phase Current
Figure 9. Three-phase stator current of the induction motor withinter-turn short circuits on one phase under full load condition.
three-phase stator currents for the induction motor with inter-turnshort-circuit are shown in Figure 9.
9.1.3. Air-gap Eccentricity
Figure 10 illustrates the frequency and time variation of the stator linecurrent under the consideration of 33.33% static air-gap eccentricity.From Eq. (24), the spectrum of the line current will have twoharmonics. The amplitude value of the stator line current will notvary and equal to its value on healthy operation.
Table 4 illustrates a comparison between the results obtained fromfinite element solution and analytical formula in Eq. (24).
Figures 11 and 12 show the waveforms of stator current in thecase of two and four broken bars, respectively. It is clear from the
1 1.05 1.1 1.15 1.2 1.25 1.3-60
-40
-20
0
20
40
60
time (s)
Sta
tor
cu
rre
nt
(A)
(a)
0 20 40 60 80 100 120 140 160 180 200-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (Hz)
A
mp
litu
de
in
dB
Normalized Amplitude spectrum in dB
LSH
-45.43 dB
RSH
-33.71 dB
3rd Harmonic
(b)
Figure 10. The stator line current under air-gap eccentricitycondition, (a) the time variation, (b) the frequency spectrum.
Progress In Electromagnetics Research B, Vol. 53, 2013 309
Table 4. A comparison between finite element solution and analyticalformula results in case of air-gap eccentricity fault.
MotorSpeed(rpm)
slipLSH (Hz) RSH (Hz)
FEMAnalyticFormula
FEMAnalyticFormula
1447 0.035333 26.14 25.88 75.36 74.6
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3-80
-60
-40
-20
0
20
40
60
80
time (s)
Sta
tor
cu
rre
nts
(A
)
Figure 11. The stator currentenvelope-two broken bars underrated load.
-80
-60
-40
-20
0
20
40
60
80
Sta
tor
cu
rre
nts
(A
)
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
time (s)
Figure 12. The stator currentenvelope-four broken bars underrated load.
figures that the envelope of the three-phase stator currents is generatedand causes a change to the general shape of the currents. Theenvelope is repeated periodically at a frequency equal to 2 Sf. Thefrequency and amplitude of the envelope are directly proportional tothe number of broken bars. Increasing the number of broken bars leadsto increasing the angular deflection for the magnetic axis of rotatingmmf. Consequently, the magnetic field of the stator is distorted andmodulates in a sequential manner.
10. MIXED FAULTS
Figures 13 and 14 show the frequency components of the stator currentair-gap eccentricity with two and four broken bars, respectively. Theharmonic components due to broken bars appear at fs(1 ± KS). Inaddition, two side-band components due to static eccentricity arelocated on fecc.
Figure 15 shows the frequency spectrum of stator current inthe case of air-gap eccentricity and inter-turn short circuit of statorwinding. These types of faults produce side-band components at the
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20 40 60 80 100 120 140 160 180 200-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
frequency (Hz)
Am
plu
in d
B
Fast Fourier Transform of the stator current in dB
-45.43
-43.29
-25.48
-28.02
-43.47
Figure 13. The stator linecurrent under air-gap eccentricitywith two broken bars condition.
20 40 60 80 100 120 140 160 180 200
frequency (Hz)
Am
plu
in
dB
Fast Fourier Transform of the stator current in dB
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
-58.69-42.43
-31.17-38.29
-56.43
Figure 14. The stator linecurrent under air-gap eccentricitywith four broken bars condition.
20 40 60 80 100 120 140 160 180 200-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
frequency (Hz)
Am
plu
in
dB
Fast Fourier Transform of the stator current in dB
-27.63
-35.37 -41.86
Figure 15. The stator line current under air-gap eccentricity with10% stator winding short circuit condition.
Table 5. Amplitude and frequency variation under faults conditions.
LSH RSHSideband
Harmonic (k = 4)dB Hz dB Hz dB Hz
Stator shortcircuit (15%)
−42.83 25.9 −40.93 74 −27 149.9
Stator shortcircuit (30%)
−42.73 26.73 −40.75 74.6 −25.06 149.9
Air-gapeccentricity
−49.36 26.14 −37.32 75.36 −46 149.9
Progress In Electromagnetics Research B, Vol. 53, 2013 311
same location (Eqs. (22) and (24)). The amplitude of the frequencycomponent at fs = 149.9Hz is grater than the fault with eccentricityor short circuit of stator winding.
11. DISCUSSION AND CONCLUSION
Finite element method provides a representation of complex geometryof the electrical machines as well as the actual non-linearity andsaturation of the core materials. As a result, this method will reducethe cost and effort for damaging a real machine.
It is clear from simulation results that the amplitude of sidebandsharmonics components will increase when the number of broken bars isincreased as shown in Figure 2 and Figure 3. In addition, the shape ofstator currents is detoured from sinusoidal waveform and has a ripplenature due to the effect of the distorted rotor MMF. The value of rippleis increased as the number of broken bars is increased.
Based on the rules for calculating the harmonics produced in statorline currents generated in the air-gap eccentricity and inter-turn shortcircuit, there are two sidebands components in the spectrum on (74and 26) Hz. The harmonic component depends on the degree of eachfault type. In order to distinguish between the two fault types, itis necessary to compare the amplitude of the stator current in timedomain. In the case of short circuit fault, the stator current will havea high value compared with air-gap eccentricity.
It is clear from the frequency spectrum that the sidebandharmonics components have greater values in the case of short circuitdue to unbalance situation in the three-phase circuit of the statorwinding. In the case of air-gap eccentricity, the unbalance rotor mmfwill inject a side-band harmonic in the balance stator currents. Due tothe inter-turn short circuit, the rotating mmf produced by unbalancedstator currents will also be unbalanced and affect the shape of rotormmf. Then the unbalanced rotor mmf will inject a side-band harmonicin the unbalanced stator current. Therefore, the amplitude of theside band harmonic in this case has a greater value than the air-gapeccentricity.
Table 5 shows the amplitudes of left and right sideband harmonicsunder different faults conditions. The value of harmonic componentmay give an exact indication about the type of fault more than thefrequency value. Due to broken rotor bars, the magnetic neutral axisof magneto motive force shifts from the normal location in the case ofhealthy motor. This deviation produces a shift in the angular positionand waveform distortion of the rotor mmf. This variation is a functionof the location as well as the number of broken bars.
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